矩形棱柱空间对角线：用直角三角形与向量求长度

GeoGebra 命令及参数

1. Textfield(a) → InputBox1
2. Textfield(b) → InputBox2
3. Textfield(c) → InputBox3
4. Textfield(d) → InputBox4
5. Textfield(f) → InputBox5
6. Textfield(g) → InputBox6
7. If(Length[Mode[l1]] ≟ 0, "No digits repeat!", "Repeated digits exist.") → text4
8. Textfield(h) → InputBox7
9. PointIn(Plane[(0, 0, 0), (1, 0, 0), (1, 1, 0)]) → D
10. Circle(D, (10 * a) + b, zAxis) → e
11. Point(e) → E
12. Line(D, E) → i
13. Rotate(D, ((-pi)) / 2, E, Plane[(0, 0, 0), (1, 0, 0), (1, 1, 0)]) → D'
14. Line(D', E) → j
15. Segment(D, E) → k
16. Circle(E, d, Line[E, E + (0, 0, 1)]) → p
17. Intersect(j, p) → F, H
18. Segment(E, H) → l
19. Angle(H, E, D) → α
20. Segment(D, H) → m
21. Line(H, H + (0, 0, 1)) → n
22. Sphere(H, c) → o
23. Intersect(n, o) → I, J
24. Segment(H, J) → q
25. Segment(J, D) → r
26. Polygon(D, E, H) → t1, h_1, d_1, e_1
27. Polygon(D, H, J) → t2, j_1, d_2, h_2
28. OrthogonalLine(J, Vector[J, D], Vector[J, H]) → s
29. Line(H, J) → t
30. Circle(J, sqrt((100 * f) + (10 * g) + h), s) → c_1
31. Point(c_1) → K
32. Segment(J, K) → f_1
33. Line(E, E + (0, 0, 1)) → g_1
34. Sphere(E, Radius[c_1]) → u
35. Sphere(E, c) → v
36. Intersect(g_1, v) → L, M
37. Line(D, d_1) → i_1
38. Sphere(D, d) → w
39. Intersect(i_1, w) → N, O
40. Translate(O, Vector[E, M]) → O'
41. Translate(D, Vector[E, M]) → D'_{1}
42. Polygon(D, O, O', D'_{1}) → q1, d_3, o_1, o', d'_{1}
43. Polygon(D'_{1}, M, E, D) → q2, k_1, m_1, e_2, d_4
44. Polygon(M, J, H, E) → q3, m_2, j_2, h_3, e_3
45. Polygon(H, J, O', O) → q4, h_4, j_3, l_1, o_2
46. Polygon(D'_{1}, M, J, O') → q5, n_1, m_3, j_4, p_1
47. Segment(O', D'_{1}) → q_1
48. Segment(D'_{1}, D) → r_1
49. Segment(D, O) → s_1
50. Segment(O, O') → t_1
51. Segment(E, M) → a_1
52. Segment(M, D'_{1}) → b_1
53. Segment(M, J) → f_2
54. Segment(J, O') → g_2
55. Segment(H, O) → i_2
56. Angle(J, H, D) → β